Question: Simplify the following expression and state the condition under which the simplification is valid. You can assume that $q \neq 0$. $k = \dfrac{10q - 70}{-3} \div \dfrac{6q(q - 7)}{2q} $
Explanation: Dividing by an expression is the same as multiplying by its inverse. $k = \dfrac{10q - 70}{-3} \times \dfrac{2q}{6q(q - 7)} $ When multiplying fractions, we multiply the numerators and the denominators. $k = \dfrac{ (10q - 70) \times 2q } { -3 \times 6q(q - 7) } $ $ k = \dfrac {2q \times 10(q - 7)} {-3 \times 6q(q - 7)} $ $ k = \dfrac{20q(q - 7)}{-18q(q - 7)} $ We can cancel the $q - 7$ so long as $q - 7 \neq 0$ Therefore $q \neq 7$ $k = \dfrac{20q \cancel{(q - 7})}{-18q \cancel{(q - 7)}} = -\dfrac{20q}{18q} = -\dfrac{10}{9} $